T?-p chI Tin h9C va Dieu khien h9C, T.16, S ?, (2000), 15-18 A I'i' A,l L~P qCH TOI U'U CHO B9 CHUYEN M~CH ATM SUo DUNG MANG NO RON . . D~NG CONG TRAM, CHU VAN HY Abstract. We consider an ATM (asynchronous transfer mode) nonblocking switch with input bypass queues. A queue length based priority scheme is used. In this paper we present a method of designing an optimal cell scheduling controller using Hopfield networks to maximize switch throughtput in ATM environments. Theo chien hro'c dieu khi~n luong ph an 16p [2] [rrnrc tg bao, rmrc cuoc goi, rmrc mang], dieu khign rmrc tg bao trtrc tigp lam thay d5i so hro ng te bao diro'c chuydn m ach d cac nut, nHm cue dai hoa thong hrong va C1).'Cti~u hoa thoi gian tr~. Neu xet theo yeu cau bi~u di~n toan h9C ch~t che nhir vay, thl cac phircng phap dieu khi~n luong va l~p lich tg bao thucrig dung, nhir: cai thung ro, cU as5 v61.dau vao tuan tV deu khOng phai la. toi U'U [2]. M9t cau hoi durrc d~t ra la: Co th~ chg t ao bi? dieu khi~n l~p lich toi iru cho cac chuydn mach ATM khOng? ngu co thl nguyen If lam vi~c ciia no ra sao? va vrri phtrong ti~n ky thu~t hieri nay, li~u thigt kg mci co kha thi khOng? Sau khi th anh l~p me hlnh toan h9C, ta nh an thay day la m9t bai toan toi U'U hoa t5 ho'p, rat it khi ton t.ai thu~t giii co hieu qui, Hen nira, ngu thirc hien bhg phan mem ho~c cirng h6a nho' cac vi m ach so thong thtrong, thl v6'i khdi hrong tinh toan do s9 ta khOng th~ tinh kip toc di? rat nhanh cti a rnang ATM. May thay, cac m,!-ng no ron nhan t ao v6'i kh a n ang tinh toan song song va nhirng tinh nang "thong minh" la nhirng corig c~ m6'i giup ta thuc hien diro'c rihiem v':! do. Cac m,!-ng Hopfield, RBF dii th anh cong cho mot so irng dung IO,!-inay trong h~ thong vi~n thOng. Trong bai nay, cluing toi gioi thieu mdt phucrng phap thigt kg bi? di'eu khign l~p lich toi iru sli- dung m~ng Hopfield [5] vo'i mdt so b5 sung va ph at tri~n m61 2. THANH L~P MO HiNH ToAN H9C Ta xet trtro'ng ho p chuygn mach co N cu'a vao, N cu'a ra, bi? d~m dau vao kigu hang vong v6'i crr ctt'a s5 W [5]. Muc dich d~t ra la circ dai h6a so cac tg bao diro'c chuye n tir cac cu'a vao sang cac ctt'a r a veri cac dieu ki~n sau: 1. Trong m6i hang cli-a s5 co nhidu nhfit 1 tg bao diro'c chon M chuydri. 2. Cac tg bao dtro c chon ph ai co dia chi nai den kh ac nhau. 3. Trong m6i hang cu a cua s5, cac tg bao co cling dia chi noi den phai tu an theo lu~t "vao triro'c ra truce" (FIFO). 4. Cac te bao 6' hang dai hen can dtroc tru tien chuydn tru'o'c, va so tg bao diro'c iru tien la nhieu nh at. Dieu kien 1 do chg di? lam vi~c cu a bi? chuye n mach qui dinh. Dieu ki~n 2 la M tranh nghen 6' cli-a ra. Cac dieu kien 3, 4 nham han che tho'i gian tr~ - ygu to co anh htro'ng xau den chat hrong phuc vu, th am chi dh den tr an b9 d~m lam mat te bao. Dia chi nai den cti a te bao dircc doc t ai cu-a vao. Bay gier ta giin cho te bao (y hang i ci?t j cu a bi? d~m bien so Xij nh an 2 gia tri nhir sau: neu tg bao diro'c chon thl Xij = 1, ngiro'c lai Xij = O. T~p cac tg bao diro'c chon S dtro'c dinh nghia: S= {XIXij= 1, iE{I, ,N}, J·E{I, ,W}}. (1) V~y bai toan l~p lich toi U'U la: TIm t~p S sac cho 16 £>A.NG CONG TRAM, CHU VAN HY N W ~~ z. + max ~~ 1,1 , i=1 j=1 (2) voi cac di'eu kien sau: 1. 2:xij::;l, Vi. (3) j 2. Cho Xij E S, Xpq E S, p =1= i, thi: Dia chi den (te bao if) =1= Dia chi den (te bao pq). (4) 3. Cho f < k, thi TU)Xij ~ T(k)Xik' Vi (5) trong d6 T(·) Ill.ham nghich bien, chi so do vi tri c9t cua te bao, 4. 2: 2: P(LdXij + max, (6) i j trong d6 P(L i ) Ill.ham dong bien voi chieu dai L; cua hang thii' i. Nhi'eu cong trinh nghien ciru dii chi ra rhg: cho cac bai toan toi iru h6a t5 hop ki~u (2)-(6) rat hiem khi ton t.ai m9t thu~t giii c6 hieu qui. Neu c6 thu~t giai thi do d9 phirc tap tinh toan Ian tho'i gian tinh se d ai - ngay d khi thuc hi~n bhg phan cli-ng - nen kh6 dap trng duoc nhirng qua trinh rat nhanh nhir cac h~ thong thong tin hi~n dai. Day Ill.li do den nay nguo'i ta vh ira dung cac b9 di"eu khie'n do n gian, thiro'ng Ill.nhirng giii phap hop H h6a ho'n Ill.toi tru. Mang no' ron nhan t<;LO voi kha nang xli- If song song, c6 m9t so tinh nang "thOng minh" do mo phong nguyen H lam vi~c cua b9 niio ngiroi, diro'c che t ao thanh nhirng vi mach cO-Ion, se Ill.m9t the h~ linh ki~n moi c6 the' giup ta giii trirc tuyen nhirng bai toan phirc tap nhtr tren [7]. 3, TOI lTU HOA SU- DVNG M~NG HOPFIELD Mang Hopfield lien tuc gom n no' ron dtroc mo ti bhg h~ phirong trinh vi ph an [3] su. u. ~ C; dt' = - ~ + Z:: Wij Vj + Ii, Wii = 0, i = 1,2, " n. j=1 (7) U; Ill.mire kich heat, C, Ill.di~n dung mang, R.; Ill.tr6- khang, Wij Ill.trong so noi vai no' ron thu- i, I; Ill.dau vao ngoai, Vi Ill.dau ra ciia no ron thtr i: Vi = a;(>'Ud. (8) Ham kich heat ai(-) don di~u tang, trtro'ng hop di~n hinh Ill.ham xich ma [3]. >. Ill.tham so khuech dai. D~ nghien ciru tinh 5n dinh ciia h~ thong (7), Hopfield dii dtra ra ham Liapunov - con goi Ill. ham nang hrong n 1 n l V ; i : E = ~ [- - ~ w·· v, V· - J. v, + -a- 1 (V) dV]. ~ 2 Z:» \J \ J \ \ >'R. i=1 j=1 0 \ (9) C6 th~ chirng minh: neu Wij = Wji, thi dE/dt < O. Nhir v~y, theo dinh If Liapunov di"eu ki~n can va du de' m<;LngHopfield 5n dinh Ill.cac trong so doi ximg. D~ dang thay dieu d6 cling dung cho d. triro'ng hop mang co cac yang tlJ.'phan hoi: Wii =1= O. Hopfield va Tank dii sorn nhm thay kha nang su- dung mang Hopfield de' giii cac bai toan toi iru (1985). Boo vi 6- xung quanh die'm 5n dinh dE/dt < 0, tu-c E luon giarn; con tai do dE/dt = 0, tire E khong giam tiep va cling khOng tang, nen die'm 5n dinh cling chinh Ill.die'm ClJ.·Cti~u [cue b9). Do d6, neu phai tim cac gia tri V,:, i = 1 , n, de' ClJ.'Ctie'u h6a ham E(V,:), ta c6 the' tien hanh theo phirong phap rnoi nhu sau: Ta xay dung m ang Hopfield tirong ling (7), vci dieu ki~n cac trong so doi ximg thi tir vi tri ban dau sau m9t thoi gian giao d9ng ngl{n m<;Lngse 5n dinh, hie do, do dau ra cd a cac no' ron ta dlIQ"Ccac gia tri Y;; phai tim. Phuong ph ap nay diro'c goi Ill.toi U'U hoa khOng thu~t toan [1]. Theo (7), (8), (9) ta c6 the' tim dlIQ"Cplnrong trinh d9ng h9C cda mang no' ron tir ham E(Y;;) cho triroc C. dU i __ aE(Y;;) . \ dt - ay;; (10) LAP qCH TOI UlJ CHO BQ CHUYEN MACH ATM SU- DlJNG MANG NO' RON 17 Trong thirc te cac h arn mvc tieu thtrong khOng co so hang chira tfch ph an nhir & (9). Luc do, M tri~t tieu anh htrorig cua no din chon khuech dai ). du Ion, va ham E co dang n 1 n E ~ '" [- - '" W·· v. V· - I· v:.] - ~ 2 ~ 'J 'J ". i=1 j=1 (11) Tru'ong hop t5ng quat E co dang ba:t ky da. dtro'c nhiElu tac gii nghien ctru. M9t vai ket qui co th~ xem & [7]. ThOng thirong bai toan toi iru hoa con co m9t so rang bU9C. Ta co th~ giii, vi du theo phtro ng phap chuydn vElbai toan khOng rang bU9C b~ng each dira VaG cac nh an trr Lagrange v.v .••.•••• ~ ,J 4. BQ DIED KHIEN L~P qCH TOI UU NO' RON Mang N X W net ron 111.phan chfnh ciia b9 di'eu khi~n. Tircng tv- nhir cac te bao trong crra s5 cua b9 d~m, ta ki hieu cac no' ron theo tea d9 trong ma tr%n N X W. Nhtr v%y, m6i net ron se turmg irng vo'i m9t te bao trong d:a s5. Neu thiet ke sac cho d'iiu ra Vij ciia net ron ij b~ng 1 (ho~c 0) ham nghia te bao tiro'ng img diroc chon [hoac khong], thl ta co quan h~ giira cac bien Vij = Xij (khi m~ng 5n dinh]. Tren CO's& do ta chuydn bai toan cue dai hoa (2) voi cac dieu ki~n (3)-(6) v'll bai toan Cl).'Cti~u hoa (9) voi cac diElu ki~n tirong irng. Liru y rhg, M don gian, trong phan 3 ta ki hieu cac net ron b~ng m9t chi so. Nhtr phan tfch & tren, dieu kien 1 111.rang bU9C dang :::;,dieu ki~n 4 lam thanh m9t ham mvc tieu phu Se 111.don gian nha:t, neu ta bi~u di~n ta:t d. cac dieu ki~n bhg cac ham rnuc tieu phu va giii bai toan da muc tieu theo phtrrrng phap chon cac trong so. Ham muc tieu (2) dtro'c chuydn thanh Eo = - L L Vij -+ min. j ve each anh xa m9t so di'eu ki~n d~c trtrng cho mang no- ron VaG ham nang hrong co th~ tham khdo [6]. 0- day ta bie'u di~n "dinh hrong hoa" cac di'llu ki~n nhir sau [5] 1. El = I: I: [K ij - I: q V iq ]2 -+ min. (13) i j (12) 2. E2 = I: I: I: I: Hij,pq Vij Vpq -+ mIn. (14) i j p q 3. E3 = I: I: T(j) Vij -+ min. (15) i j 4. E4 = "- I: I: P(L;) Vij -+ mIn. (16) i j Trong cac c6ng thirc tr en: K ij 111.dau VaG ngoai cho nO' ron ij. Neu vi tr i ij cua b9 d~m co 1 te bao thl. K ij = 1, ngiroc Iai K ij = O. Hij,pq 111.mdt phan trr ciia ma tr~n H co kich thucc NW X NW. Neu te bao ij va te bao pq co cung dia chi noi den thl Hij,pq = 1, ngiro'c lai Hij,pq = O. H 111.ma tr~n doi xirng. Cac ham T(j), P(Ld dung cho bi~u di~n cac di'eu ki~n v'll rmrc iru tien 3, 4 co th~ tinh nhir sau [5] -2j T(j)=W+1+1,1:::;j:::;W. (17) { 1 neu i; > L' P(L i ) = 0 neu L, = L' (18) -1 neu L, < L' trong do L' 111.chieu dai trung blnh cu a cac hang 1 N L' = N LL i. i=1 (19) 18 DA.NG CONG TRA-M, CHU VAN HY I)g cung c~p cac so lWu K ij , Hij,pq, T(j), P(Ld ta c'an thiet ke cac mach xu If tin hi~u phu. Ta thay El dat circ tigu neu trong m(!)ihang co nhieu nHt 1 no ron dtrcc kich heat (dau ra bhg 1). E2 = 0 khi khOng xay ra nghen If cac cU:ara. E3 co gia tri nho nhat khi cac te bao 0- cling mi?t hang co cling dia chi den tuan theo ku~t FIFO. E4 dat C1].·Ctigu neu so te bao co rrnrc U"Utien cao diroc chon 111.nhieu nhat, Ta di den giii bai toan toi U'Uco mi?t ham mvc tieu E* = AEo + B El + C E2 + DE3 - F E4 -+ rrnn, 2 2 (20) trong do A, B, C, D, E, F 111. cac trong so dtro'ng diro'c chon ph in anh "tam quan trong" cua ham mvc tieu phu, Theo (10) ta l~p diro'c phirong trinh di?ng h9C cua m~ng Hopfield. Chii y: trircc khi lay dao ham can ci?ng them VaG E* so hang chira tich phan trong (9). Ta nh~n dtro'c ket qui su., u., L L L (.) () c.·-= +A+BK·-B v:. -C H V. -DTJ +FPL·. tJ dt R.; . t) tq t),pq pq t ) q P q (21) Do ta muon If trang thai 5n dinh dau ra cua cac no ron bhg 1 hoac 0, nen phai chon ham kich heat co dang xich ma don cue voi khuech dai ). du Ion 1 Vij = aij().Uij) = 1 • __ ( 'TT \ . (22) 5. KET LU~N Tren day cluing toi da. trlnh bay phtrong phap thiet ke bi? di'eu khign l~p lich te bao toi U"U theo each nhm ch~t che cua 11 thuydt toan h9C toi U"Uhca va di'eu khign tl] "di?ng. Cac ket qui phan tich va mf phong trong [5] cling cho th~y tfnh kha thi va nhirng U"Udi~m cua phirong an no ron hoa trong dieu kien chat hro'ng cac vi mach, cling nhir toc di? yeu cau ciia m~ng ATM hi~n nay. Tuy nhien, v'e phircmg phap lu~n ta con phai lU"U Y den v~n d'e dat toi U"Utoan cue khi su dung m~ng Hopfield. 'I'ir (9) ta tHy do co them so hang chira tich phan, ham nang hrong E khOng con 111. blnh plnrong nlnr ham mvc tieu E* nira, ma 111. mi?t ham phi tuyen phtrc t ap. Vi the, m~ng no' ron co thg ro'i VaGdigm C1].·Ctigu cue bi? co mire nang hrong cao hon nang hro'ng day E min . 8rl: dung ky thu~t "u mf phong" lam cho mang co kha nang chuydn den trang thai nang hrong cao hem M thoat khoi digm C,!Cti~u cue bi? va dat dtro'c difm C,!Ctifu roan cue E min . TAl L~U THAM KHAO [1] Chu Van Hy , Toi U"Uhoa s1.l:dung m~ng no ron va irng dung trong di'eu khign t'! di?ng, Tin hoc va oa« khie'n hoc 15 (3) (1999) 18-23. [2] Gu X., Sohraby K., and Vamann D. R., Control and Performance in Packet, Circuit and ATM Networks, Kluwer Academic Publisher, 1995. [3] Lin C. T. and Lee C. 8. G., Neural Fuzzy Systems, Printice-Hall Intern'ational, 1996 [4] Nguy~n HiIu Thanh, T5ng quan ve Ky thu~t mq,ng B-ISDN, Khoa h9C va Ky thu~t, Ha Ni?i, 1997. [5] Park Y. K. and Lee G., NN based ATM cell scheduling with queue length - based priority scheme, IEEE J. Select. Areas Commun. 15 (2) (1997) 261-270. [6] Tagliarini G. A., Christ J. F., and Page E. W., Optimization using neural networks, IEEE Trans. Computers, 40 (12) (1991) 1347-1358. [7] Vidyasagar M., Minimum - seeking properties of analog neural networks with multilinear ob- jective functions, IEEE Trans. Automat. Contr. 40 (8) (1995) 1359-1375. Nh~n bai ngay 18 - 6 -1999 Nh~n lq,i sau khi slla ngay 8 -1 - 2000 Dif,ng Cong Tram, T5ng cue Bv:u ai4n. Chu Van Hy, Hoc vi4n Cong ngh4 bti"u chinh viln thong. . 15-18 A I'i' A,l L~P qCH TOI U'U CHO B9 CHUYEN M~CH ATM SUo DUNG MANG NO RON . . D~NG CONG TRAM, CHU VAN HY Abstract. We consider an ATM (asynchronous transfer mode). dlIQ"Cplnrong trinh d9ng h9C cda mang no' ron tir ham E(Y;;) cho triroc C. dU i __ aE(Y;;) . dt - ay;; (10) LAP qCH TOI UlJ CHO BQ CHUYEN MACH ATM SU- DlJNG